Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity

TL;DR

This paper introduces a near-linear computational complexity algorithm for blind source separation of sinusoidal signals, accurately estimating frequencies, amplitudes, and phases in noisy data using a maximum likelihood approach.

Contribution

The paper presents a novel multi-tone decomposition algorithm with near-linear complexity that can estimate sinusoid parameters and perform blind source separation without prior knowledge of source count.

Findings

Achieves near-linear computational complexity of  O(N).

Effectively estimates sinusoid parameters in noisy environments.

Can operate as a blind source separator without knowing the number of sources.

Abstract

We propose a multi-tone decomposition algorithm that can find the frequencies, amplitudes and phases of the fundamental sinusoids in a noisy observation sequence. Under independent identically distributed Gaussian noise, our method utilizes a maximum likelihood approach to estimate the relevant tone parameters from the contaminated observations. When estimating $M$ number of sinusoidal sources, our algorithm successively estimates their frequencies and jointly optimizes their amplitudes and phases. Our method can also be implemented as a blind source separator in the absence of the information about $M$. The computational complexity of our algorithm is near-linear, i.e., $\tilde{O}(N)$.